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Clackson scroll formula
The Clackson scroll formula,
 * $$l = \pi \cdot s \cdot n^2\, ,$$

is used in blacksmithing to estimate the length $$l$$ of stock required to produce a scroll in the form of an Archimedean spiral of $$n$$ turns with a (on-center) spacing $$s$$ between the turns. This estimate can be derived by thinking of the scroll as having a thickness of s and being wound tightly so that there is no space between the layers. When wound up the scroll is roughly a cylinder with a radius of s·n, so its cross-sectional area is roughly πr2 = πs2n2. On the other hand, the scroll's cross-sectional area whether wound up or not is l·s. Thus ls = πs2n2, or l = πsn2.